The Hawks had lost six of their last seven, including an embarrassing setback against Chicago Monday in which they scored a franchise-low 20 points in the first half.
Teague made 12-of-18 shots from the field and scored 28 points along with 11 assists. Atlanta built a 16-point cushion at intermission and boosted it to 24 during the third period.
Devin Harris added 18 points for the Hawks and Al Horford had 17 points and 13 rebounds. Atlanta, which had a 10-minute scoreless stretch against Chicago, hit 57 percent of its shots against the Nets.
Brook Lopez scored 22 points for Brooklyn, which will host Atlanta Friday.
2014: The Year in Music [PHOTOS]